A low-dimensional feature vector representation for alignment-free spatial trajectory analysis

Trajectory analysis is a central problem in the era of big data due to numerous interconnected mobile devices generating unprecedented amounts of spatio-temporal trajectories. Unfortunately, datasets of spatial trajectories are quite difficult to analyse because of the computational complexity of the various existing distance measures. A significant amount of work in comparing two trajectories stems from calculating temporal alignments of the involved spatial points. With this paper, we propose an alignment-free method of representing spatial trajectories using low-dimensional feature vectors by summarizing the combinatorics of shape-derived string sequences. Therefore, we propose to translate trajectories into strings describing the evolving shape of each trajectory, and then provide a sparse matrix representation of these strings using frequencies of adjacencies of characters (n-grams). The final feature vectors are constructed by approximating this matrix with low-dimensional column space using singular value decomposition. New trajectories can be projected into this geometry for comparison. We show that this construction leads to low-dimensional feature vectors with surprising expressive power. We illustrate the usefulness of this approach in various datasets.